Preheat the grill, setting the burners to high. Oil the grate.
On a work surface, sprinkle the dry rub onto the shoulder and rub all sides to distribute evenly. Let marinate for 15 minutes.
Grill the meat on all sides except the skin side. Remove from the heat. Wrap the shoulder in two layers of aluminum foil, making sure the foil is completely sealed.
Turn off the burners on one side of the grill. Place the meat on the side that is off so it cooks with indirect heat. Close the lid and cook for 4 hours, or until the meat is cooked and tender, maintaining a grill temperature of 400°F (200°C). Remove from the heat.
Remove the bone and the skin. Delicious served with baked sweet potatoes with onion (see recipe), honey bourbon sauce or quick barbecue sauce (see recipes).